I am trying to replicate a RBC model with technology shock

$\log(z_{t+1})=\rho \log(z_t)+\epsilon_{t+1} \ $ with $\epsilon_t \sim$ i.i.d.$ \mathcal{N}(0,\sigma^2)$ and $0 < \rho < 1$

The original source states that:

$\sigma$ is determined so that the innovation in $z^{1-\theta}$ has standard deviation 0.007

where $0 < \theta < 1$ Unfortunately, I don't know how to approach this problem with a (non-integer) exponent and what exactly is meant by the innovation in $z^{1-\theta}$

How can I (analytically) find the value of $\sigma$?

Thanks for your help!

P.S. The source is Greenwood, Rogerson, Wright (1995), "Household Production in Real Business Cycle Theory", in Frontiers of Business Cycle Research, p.167


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.